Statistics of the Zeros of the Zeta Function: Mesoscopic and Macroscopic Phenomena

We review the well known microscopic correspondence between random zeros of the Riemann zeta-function and the eigenvalues of random matrices, and discuss evidence that this correspondence
extends to larger mesoscopic collections of zeros or eigenvalues. In addition, we discuss interesting phenomena that appears in the statistics of even larger macroscopic collections of zeros. The terms microscopic, mesoscopic, and macroscopic are from random matrix theory and will be defined in the talk.